Gravitation near the Earths Surface You weigh 120 lb at the

Gravitation near the Earth\'s Surface You weigh 120 lb at the sidewalk level outside the World Trade Center in New York City. Suppose that you ride from this level to the top of one of its 1350-ft towers. How much less would you weigh there because you are slightly farther away from the center of the Earth?

Solution

Weight due to gravitational force of earth,

W = G Me m / (Re + h)^2

At Side walk:

120 = G Me m / (Re^2) ..........(i)

At tower top,

W = G Me m / (Re + 1350)^2 .........(ii)

Ii / i =>

W / 120 = Re^2 / ( Re + 1350)^2

Re = 2.09 x 10^7 ft

W / 120 = (2.09 x 10^7)^2 / (2.09x10^7 + 1350)^2

W = 119.9845 lb